Question

A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

• A. $\frac { R } { \left( \frac { g R } { 2 V ^ { 2 } } - 1 \right) }$
• B. $R \left( \frac { g R } { 2 V ^ { 2 } } - 1 \right)$
• C. $\frac { R } { \left( \frac { 2 g R } { V ^ { 2 } } - 1 \right) }$
• D. $R \left( \frac { 2 g R } { V ^ { 2 } } - 1 \right)$

Answer 1

Answer: (C)

$\frac { R } { \left( \frac { 2 g R } { V ^ { 2 } } - 1 \right) }$

Answer 2

Kinetic energy given to rocket at the surface of earth = Change in potential energy of the rocket in reaching from ground to highest point

$\Rightarrow$ $\Rightarrow$ $\Rightarrow$ $\Rightarrow$ $\Rightarrow$ $\Rightarrow$ $h = \frac { v ^ { 2 } R } { 2 g R - v ^ { 2 } }$

$\Rightarrow$ $h = \frac { R } { \left( \frac { 2 g R } { v ^ { 2 } } - 1 \right) }$